the uniformity evidenced in the other parental populations leads me to

believe that these deviations from expected behavior were probably due

to environmental effects not being normally distributed rather than

heterozygosity of the parent genotypes. These two exceptions

notwithstanding, evidence clearly demonstrated that the environment

was normally distributed.

Segregating generations. For the most part the segregating

generations were not normally distributed. All of the F2 tests had

high chi-square values, with probabilities of less than 0.001, but

backcrosses were not as consistent in their distribution (Table 3-20).

Although most did have high Chi-square values which indicated a lack

of normality, there were three backcrosses that had normal

distributions. Since the majority were not normal, these may be

ignored and further testing of the hypothesis continued.

It may be appropriate at this point to at least question and

discuss the assumptions of normality as they apply to this method.

Just because a segregating population does or does not fit the normal

distribution as it is expected to, must further testing be abandoned?

I think not, partly because of some examples which come to mind.

First of all, if a character were controlled by an additive gene

system at any number of loci, it seems that the distribution could be

normal, rather than abnormal, if alleles had equal absolute effects

and broad sense heritability were low (Figure 3-4)(2). For example, a

1:2:1 or 1:4:6:4:1 F2 segregation could be normally distributed, even

when that distribution itself is composed of other normal

distributions. Therefore it seems that, in some situations where

major genes were suspected, one could accept a normal curve in the F2

distribution and still be justified to test it. However, since the

aeschynomene data sets show little environmental variance and high

broad sense heritability, a multi-modal distribution could be

expected.

To restate the argument, the point of this example is that

distributions of a data set should be interpreted only as an indicator

of the type of inheritance. I believe that Powers is often read as

stating that homogeneous populations must always be normally

distributed and segregating populations must be not normal. But broad

sense heritability (i.e., amount of environmental variance) and type

of gene action greatly influence the distributions of segregating

populations, as illustrated in Figure 3-4. So those distributions

which do not conform to these generalities about normality should not

necessarily be considered inappropriate for partitioning. Indeed, if

major genes are suspected, partitioning may be recommended even if

some tests for normality in segregating populations do not perform as

predicted. With the aeschnomene flowering data, we hypothesized an

No Dominance HERITABILITY Dominance
75

50 -
A
100%
25-

30 40 50 60 70 80 30 40 50 60 70 80
40

30 -

20 B \
20 87.5%

10

30 40 50 60 70 80 30 40 50 60 70 80
Z 30

20

10 -

30 40 50 60 70 80 30 40 50 60 70 80
10 50%

0
30 40 50 60 70 80 30 40 50 60 70 80

25%
30 40 50 60 70 80 30 40 50 60 70 80
Units of size

Figure 3-4. Theoretical distributions in F2. The model
postulates monogenic inheritance, and that the
effect of environment varies from nil (100 per
cent heritability) to the point where environ-
mental effects account for three fourths of the
total variability (25 per cent heritability).
The left column depicts no dominance; the
right column, full dominance.
Source: Allard, R.W. 1960. Principles of
plant breeding. John Wiley and Sons, Inc.,
New York.

additive major gene system with relatively high heritability, so the

segregating populations should be abnormally distributed for the most

part. However, occasional departures from what is expected may occur

due to experimental error. In data sets which demonstrate a clear lack